Answer :
- Identify the maximum value: 208.
- Identify the minimum value: 112.
- Calculate the midrange: (208 + 112) / 2 = 160.
- The midrange is $\boxed{160}$.
### Explanation
1. Understanding the Problem
We are given the set of numbers: 146, 208, 175, 112, 193, 131. Our goal is to find the midrange of this set. The midrange is defined as the average of the maximum and minimum values in the set. So, we need to identify the maximum and minimum values first.
2. Finding the Maximum Value
First, let's identify the maximum value in the set: 146, 208, 175, 112, 193, 131. By inspection, the maximum value is 208.
3. Finding the Minimum Value
Next, let's identify the minimum value in the set: 146, 208, 175, 112, 193, 131. By inspection, the minimum value is 112.
4. Calculating the Midrange
Now, we can calculate the midrange using the formula: Midrange = (Maximum value + Minimum value) / 2. Substituting the values we found, we get: Midrange = (208 + 112) / 2 = 320 / 2 = 160.
5. Final Answer
Therefore, the midrange of the given set of numbers is 160.
### Examples
The concept of midrange can be useful in various real-life situations, such as in weather forecasting. For example, if you want to estimate the 'typical' temperature for a day, you could take the average of the highest and lowest recorded temperatures for that day. This gives you a quick and easy way to understand the central tendency of the temperature range. Similarly, in finance, you might use the midrange of the highest and lowest stock prices over a period to get a sense of the 'average' price level.
- Identify the minimum value: 112.
- Calculate the midrange: (208 + 112) / 2 = 160.
- The midrange is $\boxed{160}$.
### Explanation
1. Understanding the Problem
We are given the set of numbers: 146, 208, 175, 112, 193, 131. Our goal is to find the midrange of this set. The midrange is defined as the average of the maximum and minimum values in the set. So, we need to identify the maximum and minimum values first.
2. Finding the Maximum Value
First, let's identify the maximum value in the set: 146, 208, 175, 112, 193, 131. By inspection, the maximum value is 208.
3. Finding the Minimum Value
Next, let's identify the minimum value in the set: 146, 208, 175, 112, 193, 131. By inspection, the minimum value is 112.
4. Calculating the Midrange
Now, we can calculate the midrange using the formula: Midrange = (Maximum value + Minimum value) / 2. Substituting the values we found, we get: Midrange = (208 + 112) / 2 = 320 / 2 = 160.
5. Final Answer
Therefore, the midrange of the given set of numbers is 160.
### Examples
The concept of midrange can be useful in various real-life situations, such as in weather forecasting. For example, if you want to estimate the 'typical' temperature for a day, you could take the average of the highest and lowest recorded temperatures for that day. This gives you a quick and easy way to understand the central tendency of the temperature range. Similarly, in finance, you might use the midrange of the highest and lowest stock prices over a period to get a sense of the 'average' price level.
